This work presents a comparative study of two intelligent control strategies, fuzzy logic (FL) and artificial neural network (ANN), for energy management (BMS) within a grid-connected hybrid microgrid. The implementation and the evaluation of these intelli-gent controls were carried out using a real-world dataset under distribution grid instability constraints. The simulation results demonstrate that, while the fuzzy controller offers a faster dynamic response with high instantaneous power, it induces intensive battery loading characterized by frequent micro-cycling. On the other hand, the ANN-based control makes the power regulation smoother, thus minimizing stress on the storage system and promoting energy efficiency. The economic analysis confirms the superiority of the neural approach, revealing a 17% reduction in energy costs compared to fuzzy logic. These results highlight the crucial trade-off between response time and battery life preservation, positioning neural networks as a robust and cost-effective solution for the short-term management of smart microgrids.